Given two distinct circles with varying radii, the area of a square is 196 sq.cm, where its side length equals half the radius of the larger circle. Furthermore, the smaller circle's radius measures three-sevenths of the larger one's. What is the perimeter of the smaller circle?
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Answer: C. 24 π cm
Explanation
A square area of one hundred ninety six square centimeters gives a side length of fourteen centimeters. The larger circle radius is twenty eight centimeters since the square side equals half its radius. The smaller circle radius is twelve centimeters, yielding a perimeter of two pi times twelve or twenty four pi. The side length of a square is found by taking the square root of its total area. Circle perimeter or circumference is calculated using the formula two times pi times radius. Proportional relationships allow determining dimensions of smaller geometric figures from larger scaled shapes.
Mechanical engineers design nested circular components and square housings using proportional scaling rules. Architects incorporate geometric proportions of circles and squares into decorative floor tiling patterns. Manufacturing guidelines ensure accurate perimeters when cutting circular gaskets from raw material sheets. Option a underestimates the perimeter by using a smaller radius value from the calculation steps. Option b corresponds to an incorrect intermediate radius calculation for the smaller circle. Option d overestimates the perimeter by applying the larger circle dimensions instead.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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